Avinash Dhar

Absorption versus decay of black holes in string theory and T-symmetry

Abstract Classically a black hole can absorb but not emit energy. We discuss how this T-asymmetric property of black holes arises in the recently proposed (T-symmetric) microscopic models of black holes based on bound states of D-branes. In these string theory based models, the nonvanishing classical absorption is made possible essentially by the exponentially increasing degeneracy of quantum states with mass of the black hole. The classical limit of the absorption cross section computed in the microscopic model agrees with the result obtained from a classical analysis of a wave propagating in the background metric of the corresponding black hole (upto a numerical factor).

Sakai-Sugimoto model, tachyon condensation and chiral symmetry breaking

We modify the Sakai-Sugimoto model of chiral symmetry breaking to take into account the open string tachyon which stretches between the flavour D8-branes and -branes. There are several reasons of consistency for doing this: (i) Even if it might be reasonable to ignore the tachyon in the ultraviolet where the flavour branes and antibranes are well separated and the tachyon is small, it is likely to condense and acquire large values in the infrared where the branes meet. This takes the system far away from the perturbatively stable minimum of the Sakai-Sugimoto model; (ii) The bifundamental coupling of the tachyon to fermions of opposite chirality makes it a suitable candidate for the quark mass and chiral condensate parameters. We show that the modified Sakai-Sugimoto model with the tachyon present has a classical solution satisfying all the desired consistency properties. In this solution chiral symmetry breaking coincides with tachyon condensation. We identify the parameters corresponding to the quark mass and the chiral condensate and also briefly discuss the mesonic spectra.

New Critical Behavior in

The non-perturbative formulation of 2-dimensional quantum gravity in terms of the large-N limit of matrix models is studied to include the effects of higher order curvature terms. This leads to matrix models whose potential contains a symmetry breaking term of the form Tr ϕAϕA, where A is a given fixed matrix. This is studied in d = 0 dimensions and effectively induces additional terms of the form (Tr ϕk)2 in the one matrix potential. An exact solution to leading order of the potential V(ϕ) = 1/2 Tr ϕ2 + g/N Tr ϕ4 + g′/N2 (Tr ϕ2)2 is presented leading to 3 phases: γ = −1/2 (smooth surfaces), γ = 1/2 (branched polymer) and γ = 1/3 (intermediate phase). Including a Tr ϕ6 term in the potential gives rise to an additional phase with γ = 1/4. It is conjectured that for the general polynomial potential there are phases with γ = 1/n, n = 2, 3, …. The γ > 0 phases may correspond to c > 1 matter coupled to 2-dimensional gravity.

d=0

We show that a Nambu-Jona-Lasinio type four-fermion coupling at the z=3 Lifshitz-like fixed point in 3+1 dimensions is asymptotically free and generates a mass scale dynamically. This result is nonperturbative in the limit of a large number of fermion species. The theory is ultraviolet complete and at low energies exhibits Lorentz invariance as an emergent spacetime symmetry. Many of our results generalize to z=d in odd d spatial dimensions; z=d=1 corresponds to the Gross-Neveu model. The above mechanism of mass generation has potential applications to the fermion mass problem and to dynamical electroweak symmetry breaking. We present a scenario in which a composite Higgs field arises from a condensate of these fermions, which then couples to quarks and leptons of the standard model. Such a scenario could eliminate the need for the Higgs potential and the associated hierarchy problem. We also show that the axial anomaly formula at z=3 coincides with the usual one in the relativistic domain.

Large

We apply the method of coadjoint orbits of W∞-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum phase space distribution of the Fermi fluid. The action has an infinite series of expansion in the string coupling, which to leading order reduces to the previously discussed geometric action for the classical Fermi fluid based on the group w∞ of area-preserving diffeomorphisms. We briefly discuss the strong coupling limit of the string theory which, unlike the weak coupling regime, does not seem to admit a two-dimensional space-time picture. Our methods are equally applicable to interacting fermions in one dimension.

N

We present a nonrelativistic fermionic field theory in two dimensions coupled to external gauge fields. The singlet sector of the c=1 matrix model corresponds to a specific external gauge field. The gauge theory is one-dimensional (time) and the space coordinate is treated as a group index. The generators of the gauge algebra are polynomials in the single particle momentum and position operators and they form the group . There are corresponding Ward identities and residual gauge transformations that leave the external gauge fields invariant. We discuss the realization of the residual symmetries in the Minkowski time theory and conclude that the symmetries generated by the polynomial basis are not realized. We motivate and present an analytic continuation of the model which realizes the group of residual symmetries. We consider the classical limit of this theory and make the correspondence with the discrete states of the c=1 (Euclidean time) Liouville theory. We explain the appearance of the SL(2) structure in . We also present all the Euclidean classical solutions and the classical action in the classical phase space. A possible relation of this theory to the N=2 string theory and also self-dual Einstein gravity in four dimensions is pointed out.

Matrix Models

We discuss some physical aspects of W gravities and W strings. We identify global characteristics in W gravities (in addition to the usual Euler characteristic) and show how the dependence of the partition function on the various chemical potentials involves these quantities. We find the operators which create physical states in W3 and W4 gravities and discuss their relationship with screening operators. W strings are discussed in the framework of a natural way of coupling “matter” to W gravity, and the issues of extra dimensions and critical dimensions are clarified. We find a remarkable relationship between pure W gravities and ordinary gravity coupled to c<1 unitary minimal models.

Asymptotically free four-fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point

In this note we discuss local gauge-invariant operators in noncommutative gauge theories. Inspired by the connection of these theories with the Matrix model, we give a simple construction of a complete set of gauge-invariant operators. We make connection with the recent discussions of candidate operators which are dual to closed strings modes. We also discuss large Wilson loops which in the limit of vanishing noncommutativity, reduce to the closed Wilson loops of the ordinary gauge theory.

Non-relativistic Fermions, Coadjoint Orbits of W ∞ and String Field Theory at c = 1

We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the Hilbert space. In the bosonized theory the finiteness of the number of fermions appears as an ultraviolet cut-off. We discuss implications of this for the bosonized theory. We also discuss applications of our bosonization to one-dimensional fermion systems dual to (sectors of) string theory such as LLM geometries and c = 1 matrix model.

GAUGE THEORY FORMULATION OF THE c=1 MATRIX MODEL: SYMMETRIES AND DISCRETE STATES

The D1/D5 system is considered in the presence of the NS B field. An explicit supergravity solution in the asymptotically flat and near horizon limits is presented. Explicit mass formulae are presented in both cases. This solution has no D3 source branes and represents a true bound state of the D1/D5 system. We study the motion of a separated D1-brane in the background geometry described above and reproduce the Liouville potential that binds the D1 brane. A gauge theory analysis is also presented in the presence of Fayet–Iliopoulos (FI) parameters which can be identified with the self-dual part of the NS B field. In the case of a single D5-brane and an arbitrary number of D1-branes we can demonstrate the existence of a bound state in the Higgs branch. We also point out the connection of the SCFT on the resolved SymQ1Q5(T4) with recent developments in non-commutative Yang–Mills theory.